Today, why did Europe emerge like an express train
from the medieval age? The University of Houston's
College of Engineering presents this series about
the machines that make our civilization run, and
the people whose ingenuity created them.

Alfred Crosby looks at
medieval Europe -- a cultural backwater by
comparison with Islam and China. Then, by the 17th
century, Europe had become the most technically
advanced civilization in the world. So how did she
change so abruptly between 1250 and 1600?

Others've asked the same question. If you'd asked
me, I'd have said the change was driven by a set of
new visual arts. Crosby includes those arts, but he
sees something else that hasn't been given its due.
He looks at quantification -- reducing nature and
human activity to number. He titles his book,
The Measure of Reality.

Take numbers: medieval scholars used only Roman
numerals. The algorithms of arithmetic,
multiplication and division, are hopelessly
cumbersome without the concept of zero, and the
Romans had no zero. The Mayans did, by the way, but
Europe didn't know about that. Our zero came out of
India, and was picked up by the Arabs.

The Arabs invented most of our arithmetic methods
and they gave us the numerals that went with them.
Their system, so obviously superior, entered the
Renaissance on little cat feet, making small
inroads here and there. It wasn't fully in place
until 1600.

But other forms of exact measure were also
evolving. Visualization was a matter of measure.
Medieval artists hadn't sought to represent, but to
evoke. A medieval artist might make the relative
sizes of figures according to their importance
instead of their positioning in the foreground or
background. Then, 15th-century Italian artists
perfected perspective drawing and gave us a way to
measure reality by showing how things really look.

Finally, in 1525, Albrecht Dürer turned
Italian perspective into our modern science of
descriptive geometry, and art literally became a
new form of mathematics.

Early medieval music was oddly without measure. The
duplet and triplet patterns of Gregorian Chant go
on, without drama, drawing us into contemplation.
It's not about progress, it's about a timeless God.
Modern musical notation evolved between 1250 and
1600 and its main feature is measure. Our notes
measure time. In fact, music historians call it
mensural notation. After 1600, music seemed to be
going somewhere -- to the beat of musical measures.

And so we progressed to a new drum. We invented the
mechanical clock and we invented bookkeeping. Today, we look at
all our so-called progress with justifiable
suspicion. Are we really better developed as human
beings than our medieval forbears were?

At the same time, our young are losing the focused
quantitative sense that got us here, and that's
frightening. No one would argue that quantification
makes us more humane. But we might well fear for
what we'll become if we try to leave measure behind
-- now that we've reached this stage of our being.

I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.

(Theme music)

Crosby, A. W., The Measure of Reality:
Quantification and Western Society. New York:
Cambridge University Press, 1997.

I am grateful to Jim Bell, KUHF Radio, for
suggesting the topic and lending me his copy of the
Crosby book, and to Sohel Mahmud Reza for his paper
in UH course MECE 3301, "Numerical Systems and the
Introduction of Zero."